Abstract

We demonstrated the Talbot effect using a broadband hard x-ray beam (Δλ/λ ~1). The exit wave-field of the x-ray beam passing through a grating with a sub micro-meter scale period was successfully replicated and recorded at effective Talbot distance, ZT. The period was reduced to half at ZT/4 and 3/4ZT, and the phase reversal was observed at ZT/2. The propagating wave-field recorded on photoresists was consistent with a simulated result.

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  1. H. F. Talbot, “Facts Relating to Optical Science,” Philos. Mag. 9, 401–407 (1836).
  2. L. Rayleigh, “On Copying Diffraction-Gratings, and some Phenomena Connected Therewith,” Philos. Mag. 11, 196 (1881).
  3. M. S. Chapman, C. R. Ekstrom, T. D. Hammond, J. Schmiedmayer, B. E. Tannian, S. Wehinger, and D. E. Pritchard, “Near-field imaging of atom diffraction gratings: The atomic Talbot effect,” Phys. Rev. A 51(1), R14–R17 (1995).
    [CrossRef] [PubMed]
  4. L. Deng, E. W. Hagley, J. Denschlag, J. E. Simsarian, M. Edwards, C. W. Clark, K. Helmerson, S. L. Rolston, and W. D. Phillips, “Temporal, Matter-Wave-Dispersion Talbot Effect,” Phys. Rev. Lett. 83(26), 5407–5411 (1999).
    [CrossRef]
  5. B. Brezger, L. Hackermüller, S. Uttenthaler, J. Petschinka, M. Arndt, and A. Zeilinger, “Matter-wave interferometer for large molecules,” Phys. Rev. Lett. 88(10), 100404 (2002).
    [CrossRef] [PubMed]
  6. F. Pfeiffer, T. Weitkamp, O. Bunk, and C. David, “Phase retrieval and differential phase-contrast imaging with low-brilliance X-ray sources,” Nature 2, 258–261 (2006).
  7. W. Yashiro, Y. Takeda, A. Takeuchi, Y. Suzuki, and A. Momose, “Hard-X-ray phase-difference microscopy using a fresnel zone plate and a transmission grating,” Phys. Rev. Lett. 103(18), 180801 (2009).
    [CrossRef] [PubMed]
  8. W. B. Case, M. Tomandl, S. Deachapunya, and M. Arndt, “Realization of optical carpets in the Talbot and Talbot-Lau configurations,” Opt. Express 17(23), 20966–20974 (2009).
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    [CrossRef] [PubMed]
  11. C. Liu, R. Conley, A. T. Macrander, J. Maser, H. C. Kang, M. A. Zurbuchen, and G. B. Stephenson, “Depth-graded multilayers for application in transmission geometry as linear zone plates,” J. Appl. Phys. 98(11), 113519 (2005).
    [CrossRef]
  12. H. C. Kang, G. B. Stephenson, C. Liu, R. Conley, R. Khachatryan, M. Wieczorek, A. T. Macrander, H. Yan, J. Maser, J. Hiller, and R. Koritala, “Sectioning of multilayers to make a multilayer Laue lens,” Rev. Sci. Instrum. 78(4), 046103 (2007).
    [CrossRef] [PubMed]
  13. Filter Transmission, http://henke.lbl.gov/optical_constants/filter2.html
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    [CrossRef]
  15. J. W. Goodman, Introduction to Fourier optics (Roberts & Company, 2005).
  16. K. Suzuki, and B. W. Smith, Microlithography: Science and Technology (CRC Press, 2007).
  17. X-ray Form Factor, Attenuation, and Scattering Tables, http://physics.nist.gov/cgi-bin/ffast/ffast.pl?Z=14&Formula=&gtype=5&range=S&lower=2.4848&upper=24.848&density=2.33

2009 (2)

W. Yashiro, Y. Takeda, A. Takeuchi, Y. Suzuki, and A. Momose, “Hard-X-ray phase-difference microscopy using a fresnel zone plate and a transmission grating,” Phys. Rev. Lett. 103(18), 180801 (2009).
[CrossRef] [PubMed]

W. B. Case, M. Tomandl, S. Deachapunya, and M. Arndt, “Realization of optical carpets in the Talbot and Talbot-Lau configurations,” Opt. Express 17(23), 20966–20974 (2009).
[CrossRef] [PubMed]

2007 (1)

H. C. Kang, G. B. Stephenson, C. Liu, R. Conley, R. Khachatryan, M. Wieczorek, A. T. Macrander, H. Yan, J. Maser, J. Hiller, and R. Koritala, “Sectioning of multilayers to make a multilayer Laue lens,” Rev. Sci. Instrum. 78(4), 046103 (2007).
[CrossRef] [PubMed]

2006 (1)

F. Pfeiffer, T. Weitkamp, O. Bunk, and C. David, “Phase retrieval and differential phase-contrast imaging with low-brilliance X-ray sources,” Nature 2, 258–261 (2006).

2005 (1)

C. Liu, R. Conley, A. T. Macrander, J. Maser, H. C. Kang, M. A. Zurbuchen, and G. B. Stephenson, “Depth-graded multilayers for application in transmission geometry as linear zone plates,” J. Appl. Phys. 98(11), 113519 (2005).
[CrossRef]

2003 (2)

2002 (1)

B. Brezger, L. Hackermüller, S. Uttenthaler, J. Petschinka, M. Arndt, and A. Zeilinger, “Matter-wave interferometer for large molecules,” Phys. Rev. Lett. 88(10), 100404 (2002).
[CrossRef] [PubMed]

1999 (1)

L. Deng, E. W. Hagley, J. Denschlag, J. E. Simsarian, M. Edwards, C. W. Clark, K. Helmerson, S. L. Rolston, and W. D. Phillips, “Temporal, Matter-Wave-Dispersion Talbot Effect,” Phys. Rev. Lett. 83(26), 5407–5411 (1999).
[CrossRef]

1997 (1)

1995 (1)

M. S. Chapman, C. R. Ekstrom, T. D. Hammond, J. Schmiedmayer, B. E. Tannian, S. Wehinger, and D. E. Pritchard, “Near-field imaging of atom diffraction gratings: The atomic Talbot effect,” Phys. Rev. A 51(1), R14–R17 (1995).
[CrossRef] [PubMed]

1881 (1)

L. Rayleigh, “On Copying Diffraction-Gratings, and some Phenomena Connected Therewith,” Philos. Mag. 11, 196 (1881).

1836 (1)

H. F. Talbot, “Facts Relating to Optical Science,” Philos. Mag. 9, 401–407 (1836).

Alves, F.

Arndt, M.

W. B. Case, M. Tomandl, S. Deachapunya, and M. Arndt, “Realization of optical carpets in the Talbot and Talbot-Lau configurations,” Opt. Express 17(23), 20966–20974 (2009).
[CrossRef] [PubMed]

B. Brezger, L. Hackermüller, S. Uttenthaler, J. Petschinka, M. Arndt, and A. Zeilinger, “Matter-wave interferometer for large molecules,” Phys. Rev. Lett. 88(10), 100404 (2002).
[CrossRef] [PubMed]

Baruchel, J.

Brezger, B.

B. Brezger, L. Hackermüller, S. Uttenthaler, J. Petschinka, M. Arndt, and A. Zeilinger, “Matter-wave interferometer for large molecules,” Phys. Rev. Lett. 88(10), 100404 (2002).
[CrossRef] [PubMed]

Bunk, O.

F. Pfeiffer, T. Weitkamp, O. Bunk, and C. David, “Phase retrieval and differential phase-contrast imaging with low-brilliance X-ray sources,” Nature 2, 258–261 (2006).

Case, W. B.

Chapman, M. S.

M. S. Chapman, C. R. Ekstrom, T. D. Hammond, J. Schmiedmayer, B. E. Tannian, S. Wehinger, and D. E. Pritchard, “Near-field imaging of atom diffraction gratings: The atomic Talbot effect,” Phys. Rev. A 51(1), R14–R17 (1995).
[CrossRef] [PubMed]

Clark, C. W.

L. Deng, E. W. Hagley, J. Denschlag, J. E. Simsarian, M. Edwards, C. W. Clark, K. Helmerson, S. L. Rolston, and W. D. Phillips, “Temporal, Matter-Wave-Dispersion Talbot Effect,” Phys. Rev. Lett. 83(26), 5407–5411 (1999).
[CrossRef]

Cloetens, P.

Conley, R.

H. C. Kang, G. B. Stephenson, C. Liu, R. Conley, R. Khachatryan, M. Wieczorek, A. T. Macrander, H. Yan, J. Maser, J. Hiller, and R. Koritala, “Sectioning of multilayers to make a multilayer Laue lens,” Rev. Sci. Instrum. 78(4), 046103 (2007).
[CrossRef] [PubMed]

C. Liu, R. Conley, A. T. Macrander, J. Maser, H. C. Kang, M. A. Zurbuchen, and G. B. Stephenson, “Depth-graded multilayers for application in transmission geometry as linear zone plates,” J. Appl. Phys. 98(11), 113519 (2005).
[CrossRef]

David, C.

F. Pfeiffer, T. Weitkamp, O. Bunk, and C. David, “Phase retrieval and differential phase-contrast imaging with low-brilliance X-ray sources,” Nature 2, 258–261 (2006).

De Martino, C.

Deachapunya, S.

Deng, L.

L. Deng, E. W. Hagley, J. Denschlag, J. E. Simsarian, M. Edwards, C. W. Clark, K. Helmerson, S. L. Rolston, and W. D. Phillips, “Temporal, Matter-Wave-Dispersion Talbot Effect,” Phys. Rev. Lett. 83(26), 5407–5411 (1999).
[CrossRef]

Denschlag, J.

L. Deng, E. W. Hagley, J. Denschlag, J. E. Simsarian, M. Edwards, C. W. Clark, K. Helmerson, S. L. Rolston, and W. D. Phillips, “Temporal, Matter-Wave-Dispersion Talbot Effect,” Phys. Rev. Lett. 83(26), 5407–5411 (1999).
[CrossRef]

Di Mambro, E.

Edwards, M.

L. Deng, E. W. Hagley, J. Denschlag, J. E. Simsarian, M. Edwards, C. W. Clark, K. Helmerson, S. L. Rolston, and W. D. Phillips, “Temporal, Matter-Wave-Dispersion Talbot Effect,” Phys. Rev. Lett. 83(26), 5407–5411 (1999).
[CrossRef]

Ekstrom, C. R.

M. S. Chapman, C. R. Ekstrom, T. D. Hammond, J. Schmiedmayer, B. E. Tannian, S. Wehinger, and D. E. Pritchard, “Near-field imaging of atom diffraction gratings: The atomic Talbot effect,” Phys. Rev. A 51(1), R14–R17 (1995).
[CrossRef] [PubMed]

Guérineau, N.

Guigay, J. P.

Hackermüller, L.

B. Brezger, L. Hackermüller, S. Uttenthaler, J. Petschinka, M. Arndt, and A. Zeilinger, “Matter-wave interferometer for large molecules,” Phys. Rev. Lett. 88(10), 100404 (2002).
[CrossRef] [PubMed]

Hagley, E. W.

L. Deng, E. W. Hagley, J. Denschlag, J. E. Simsarian, M. Edwards, C. W. Clark, K. Helmerson, S. L. Rolston, and W. D. Phillips, “Temporal, Matter-Wave-Dispersion Talbot Effect,” Phys. Rev. Lett. 83(26), 5407–5411 (1999).
[CrossRef]

Hammond, T. D.

M. S. Chapman, C. R. Ekstrom, T. D. Hammond, J. Schmiedmayer, B. E. Tannian, S. Wehinger, and D. E. Pritchard, “Near-field imaging of atom diffraction gratings: The atomic Talbot effect,” Phys. Rev. A 51(1), R14–R17 (1995).
[CrossRef] [PubMed]

Helmerson, K.

L. Deng, E. W. Hagley, J. Denschlag, J. E. Simsarian, M. Edwards, C. W. Clark, K. Helmerson, S. L. Rolston, and W. D. Phillips, “Temporal, Matter-Wave-Dispersion Talbot Effect,” Phys. Rev. Lett. 83(26), 5407–5411 (1999).
[CrossRef]

Hiller, J.

H. C. Kang, G. B. Stephenson, C. Liu, R. Conley, R. Khachatryan, M. Wieczorek, A. T. Macrander, H. Yan, J. Maser, J. Hiller, and R. Koritala, “Sectioning of multilayers to make a multilayer Laue lens,” Rev. Sci. Instrum. 78(4), 046103 (2007).
[CrossRef] [PubMed]

Kang, H. C.

H. C. Kang, G. B. Stephenson, C. Liu, R. Conley, R. Khachatryan, M. Wieczorek, A. T. Macrander, H. Yan, J. Maser, J. Hiller, and R. Koritala, “Sectioning of multilayers to make a multilayer Laue lens,” Rev. Sci. Instrum. 78(4), 046103 (2007).
[CrossRef] [PubMed]

C. Liu, R. Conley, A. T. Macrander, J. Maser, H. C. Kang, M. A. Zurbuchen, and G. B. Stephenson, “Depth-graded multilayers for application in transmission geometry as linear zone plates,” J. Appl. Phys. 98(11), 113519 (2005).
[CrossRef]

Khachatryan, R.

H. C. Kang, G. B. Stephenson, C. Liu, R. Conley, R. Khachatryan, M. Wieczorek, A. T. Macrander, H. Yan, J. Maser, J. Hiller, and R. Koritala, “Sectioning of multilayers to make a multilayer Laue lens,” Rev. Sci. Instrum. 78(4), 046103 (2007).
[CrossRef] [PubMed]

Koritala, R.

H. C. Kang, G. B. Stephenson, C. Liu, R. Conley, R. Khachatryan, M. Wieczorek, A. T. Macrander, H. Yan, J. Maser, J. Hiller, and R. Koritala, “Sectioning of multilayers to make a multilayer Laue lens,” Rev. Sci. Instrum. 78(4), 046103 (2007).
[CrossRef] [PubMed]

Lee, K.

K. Lee and S. S. Lee, “Deep X-ray mask with integrated actuator for 3D microfabrication,” Sens. Actuators A Phys. 108(1-3), 121–127 (2003).
[CrossRef]

Lee, S. S.

K. Lee and S. S. Lee, “Deep X-ray mask with integrated actuator for 3D microfabrication,” Sens. Actuators A Phys. 108(1-3), 121–127 (2003).
[CrossRef]

Liu, C.

H. C. Kang, G. B. Stephenson, C. Liu, R. Conley, R. Khachatryan, M. Wieczorek, A. T. Macrander, H. Yan, J. Maser, J. Hiller, and R. Koritala, “Sectioning of multilayers to make a multilayer Laue lens,” Rev. Sci. Instrum. 78(4), 046103 (2007).
[CrossRef] [PubMed]

C. Liu, R. Conley, A. T. Macrander, J. Maser, H. C. Kang, M. A. Zurbuchen, and G. B. Stephenson, “Depth-graded multilayers for application in transmission geometry as linear zone plates,” J. Appl. Phys. 98(11), 113519 (2005).
[CrossRef]

Macrander, A. T.

H. C. Kang, G. B. Stephenson, C. Liu, R. Conley, R. Khachatryan, M. Wieczorek, A. T. Macrander, H. Yan, J. Maser, J. Hiller, and R. Koritala, “Sectioning of multilayers to make a multilayer Laue lens,” Rev. Sci. Instrum. 78(4), 046103 (2007).
[CrossRef] [PubMed]

C. Liu, R. Conley, A. T. Macrander, J. Maser, H. C. Kang, M. A. Zurbuchen, and G. B. Stephenson, “Depth-graded multilayers for application in transmission geometry as linear zone plates,” J. Appl. Phys. 98(11), 113519 (2005).
[CrossRef]

Maser, J.

H. C. Kang, G. B. Stephenson, C. Liu, R. Conley, R. Khachatryan, M. Wieczorek, A. T. Macrander, H. Yan, J. Maser, J. Hiller, and R. Koritala, “Sectioning of multilayers to make a multilayer Laue lens,” Rev. Sci. Instrum. 78(4), 046103 (2007).
[CrossRef] [PubMed]

C. Liu, R. Conley, A. T. Macrander, J. Maser, H. C. Kang, M. A. Zurbuchen, and G. B. Stephenson, “Depth-graded multilayers for application in transmission geometry as linear zone plates,” J. Appl. Phys. 98(11), 113519 (2005).
[CrossRef]

Momose, A.

W. Yashiro, Y. Takeda, A. Takeuchi, Y. Suzuki, and A. Momose, “Hard-X-ray phase-difference microscopy using a fresnel zone plate and a transmission grating,” Phys. Rev. Lett. 103(18), 180801 (2009).
[CrossRef] [PubMed]

Petschinka, J.

B. Brezger, L. Hackermüller, S. Uttenthaler, J. Petschinka, M. Arndt, and A. Zeilinger, “Matter-wave interferometer for large molecules,” Phys. Rev. Lett. 88(10), 100404 (2002).
[CrossRef] [PubMed]

Pfeiffer, F.

F. Pfeiffer, T. Weitkamp, O. Bunk, and C. David, “Phase retrieval and differential phase-contrast imaging with low-brilliance X-ray sources,” Nature 2, 258–261 (2006).

Phillips, W. D.

L. Deng, E. W. Hagley, J. Denschlag, J. E. Simsarian, M. Edwards, C. W. Clark, K. Helmerson, S. L. Rolston, and W. D. Phillips, “Temporal, Matter-Wave-Dispersion Talbot Effect,” Phys. Rev. Lett. 83(26), 5407–5411 (1999).
[CrossRef]

Primot, J.

Pritchard, D. E.

M. S. Chapman, C. R. Ekstrom, T. D. Hammond, J. Schmiedmayer, B. E. Tannian, S. Wehinger, and D. E. Pritchard, “Near-field imaging of atom diffraction gratings: The atomic Talbot effect,” Phys. Rev. A 51(1), R14–R17 (1995).
[CrossRef] [PubMed]

Rayleigh, L.

L. Rayleigh, “On Copying Diffraction-Gratings, and some Phenomena Connected Therewith,” Philos. Mag. 11, 196 (1881).

Rolston, S. L.

L. Deng, E. W. Hagley, J. Denschlag, J. E. Simsarian, M. Edwards, C. W. Clark, K. Helmerson, S. L. Rolston, and W. D. Phillips, “Temporal, Matter-Wave-Dispersion Talbot Effect,” Phys. Rev. Lett. 83(26), 5407–5411 (1999).
[CrossRef]

Schlenker, M.

Schmiedmayer, J.

M. S. Chapman, C. R. Ekstrom, T. D. Hammond, J. Schmiedmayer, B. E. Tannian, S. Wehinger, and D. E. Pritchard, “Near-field imaging of atom diffraction gratings: The atomic Talbot effect,” Phys. Rev. A 51(1), R14–R17 (1995).
[CrossRef] [PubMed]

Simsarian, J. E.

L. Deng, E. W. Hagley, J. Denschlag, J. E. Simsarian, M. Edwards, C. W. Clark, K. Helmerson, S. L. Rolston, and W. D. Phillips, “Temporal, Matter-Wave-Dispersion Talbot Effect,” Phys. Rev. Lett. 83(26), 5407–5411 (1999).
[CrossRef]

Stephenson, G. B.

H. C. Kang, G. B. Stephenson, C. Liu, R. Conley, R. Khachatryan, M. Wieczorek, A. T. Macrander, H. Yan, J. Maser, J. Hiller, and R. Koritala, “Sectioning of multilayers to make a multilayer Laue lens,” Rev. Sci. Instrum. 78(4), 046103 (2007).
[CrossRef] [PubMed]

C. Liu, R. Conley, A. T. Macrander, J. Maser, H. C. Kang, M. A. Zurbuchen, and G. B. Stephenson, “Depth-graded multilayers for application in transmission geometry as linear zone plates,” J. Appl. Phys. 98(11), 113519 (2005).
[CrossRef]

Suzuki, Y.

W. Yashiro, Y. Takeda, A. Takeuchi, Y. Suzuki, and A. Momose, “Hard-X-ray phase-difference microscopy using a fresnel zone plate and a transmission grating,” Phys. Rev. Lett. 103(18), 180801 (2009).
[CrossRef] [PubMed]

Takeda, Y.

W. Yashiro, Y. Takeda, A. Takeuchi, Y. Suzuki, and A. Momose, “Hard-X-ray phase-difference microscopy using a fresnel zone plate and a transmission grating,” Phys. Rev. Lett. 103(18), 180801 (2009).
[CrossRef] [PubMed]

Takeuchi, A.

W. Yashiro, Y. Takeda, A. Takeuchi, Y. Suzuki, and A. Momose, “Hard-X-ray phase-difference microscopy using a fresnel zone plate and a transmission grating,” Phys. Rev. Lett. 103(18), 180801 (2009).
[CrossRef] [PubMed]

Talbot, H. F.

H. F. Talbot, “Facts Relating to Optical Science,” Philos. Mag. 9, 401–407 (1836).

Tannian, B. E.

M. S. Chapman, C. R. Ekstrom, T. D. Hammond, J. Schmiedmayer, B. E. Tannian, S. Wehinger, and D. E. Pritchard, “Near-field imaging of atom diffraction gratings: The atomic Talbot effect,” Phys. Rev. A 51(1), R14–R17 (1995).
[CrossRef] [PubMed]

Tomandl, M.

Uttenthaler, S.

B. Brezger, L. Hackermüller, S. Uttenthaler, J. Petschinka, M. Arndt, and A. Zeilinger, “Matter-wave interferometer for large molecules,” Phys. Rev. Lett. 88(10), 100404 (2002).
[CrossRef] [PubMed]

Wehinger, S.

M. S. Chapman, C. R. Ekstrom, T. D. Hammond, J. Schmiedmayer, B. E. Tannian, S. Wehinger, and D. E. Pritchard, “Near-field imaging of atom diffraction gratings: The atomic Talbot effect,” Phys. Rev. A 51(1), R14–R17 (1995).
[CrossRef] [PubMed]

Weitkamp, T.

F. Pfeiffer, T. Weitkamp, O. Bunk, and C. David, “Phase retrieval and differential phase-contrast imaging with low-brilliance X-ray sources,” Nature 2, 258–261 (2006).

Wieczorek, M.

H. C. Kang, G. B. Stephenson, C. Liu, R. Conley, R. Khachatryan, M. Wieczorek, A. T. Macrander, H. Yan, J. Maser, J. Hiller, and R. Koritala, “Sectioning of multilayers to make a multilayer Laue lens,” Rev. Sci. Instrum. 78(4), 046103 (2007).
[CrossRef] [PubMed]

Yan, H.

H. C. Kang, G. B. Stephenson, C. Liu, R. Conley, R. Khachatryan, M. Wieczorek, A. T. Macrander, H. Yan, J. Maser, J. Hiller, and R. Koritala, “Sectioning of multilayers to make a multilayer Laue lens,” Rev. Sci. Instrum. 78(4), 046103 (2007).
[CrossRef] [PubMed]

Yashiro, W.

W. Yashiro, Y. Takeda, A. Takeuchi, Y. Suzuki, and A. Momose, “Hard-X-ray phase-difference microscopy using a fresnel zone plate and a transmission grating,” Phys. Rev. Lett. 103(18), 180801 (2009).
[CrossRef] [PubMed]

Zeilinger, A.

B. Brezger, L. Hackermüller, S. Uttenthaler, J. Petschinka, M. Arndt, and A. Zeilinger, “Matter-wave interferometer for large molecules,” Phys. Rev. Lett. 88(10), 100404 (2002).
[CrossRef] [PubMed]

Zurbuchen, M. A.

C. Liu, R. Conley, A. T. Macrander, J. Maser, H. C. Kang, M. A. Zurbuchen, and G. B. Stephenson, “Depth-graded multilayers for application in transmission geometry as linear zone plates,” J. Appl. Phys. 98(11), 113519 (2005).
[CrossRef]

J. Appl. Phys. (1)

C. Liu, R. Conley, A. T. Macrander, J. Maser, H. C. Kang, M. A. Zurbuchen, and G. B. Stephenson, “Depth-graded multilayers for application in transmission geometry as linear zone plates,” J. Appl. Phys. 98(11), 113519 (2005).
[CrossRef]

Nature (1)

F. Pfeiffer, T. Weitkamp, O. Bunk, and C. David, “Phase retrieval and differential phase-contrast imaging with low-brilliance X-ray sources,” Nature 2, 258–261 (2006).

Opt. Express (2)

Opt. Lett. (1)

Philos. Mag. (2)

H. F. Talbot, “Facts Relating to Optical Science,” Philos. Mag. 9, 401–407 (1836).

L. Rayleigh, “On Copying Diffraction-Gratings, and some Phenomena Connected Therewith,” Philos. Mag. 11, 196 (1881).

Phys. Rev. A (1)

M. S. Chapman, C. R. Ekstrom, T. D. Hammond, J. Schmiedmayer, B. E. Tannian, S. Wehinger, and D. E. Pritchard, “Near-field imaging of atom diffraction gratings: The atomic Talbot effect,” Phys. Rev. A 51(1), R14–R17 (1995).
[CrossRef] [PubMed]

Phys. Rev. Lett. (3)

L. Deng, E. W. Hagley, J. Denschlag, J. E. Simsarian, M. Edwards, C. W. Clark, K. Helmerson, S. L. Rolston, and W. D. Phillips, “Temporal, Matter-Wave-Dispersion Talbot Effect,” Phys. Rev. Lett. 83(26), 5407–5411 (1999).
[CrossRef]

B. Brezger, L. Hackermüller, S. Uttenthaler, J. Petschinka, M. Arndt, and A. Zeilinger, “Matter-wave interferometer for large molecules,” Phys. Rev. Lett. 88(10), 100404 (2002).
[CrossRef] [PubMed]

W. Yashiro, Y. Takeda, A. Takeuchi, Y. Suzuki, and A. Momose, “Hard-X-ray phase-difference microscopy using a fresnel zone plate and a transmission grating,” Phys. Rev. Lett. 103(18), 180801 (2009).
[CrossRef] [PubMed]

Rev. Sci. Instrum. (1)

H. C. Kang, G. B. Stephenson, C. Liu, R. Conley, R. Khachatryan, M. Wieczorek, A. T. Macrander, H. Yan, J. Maser, J. Hiller, and R. Koritala, “Sectioning of multilayers to make a multilayer Laue lens,” Rev. Sci. Instrum. 78(4), 046103 (2007).
[CrossRef] [PubMed]

Sens. Actuators A Phys. (1)

K. Lee and S. S. Lee, “Deep X-ray mask with integrated actuator for 3D microfabrication,” Sens. Actuators A Phys. 108(1-3), 121–127 (2003).
[CrossRef]

Other (4)

J. W. Goodman, Introduction to Fourier optics (Roberts & Company, 2005).

K. Suzuki, and B. W. Smith, Microlithography: Science and Technology (CRC Press, 2007).

X-ray Form Factor, Attenuation, and Scattering Tables, http://physics.nist.gov/cgi-bin/ffast/ffast.pl?Z=14&Formula=&gtype=5&range=S&lower=2.4848&upper=24.848&density=2.33

Filter Transmission, http://henke.lbl.gov/optical_constants/filter2.html

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